math five lp - pdf

8/13/2019 Math Five Lp - PDF

1/371


2/371

ii

Lesson Guides in Elementary MathematicsGrade V

Copyright 2003All rights reserved. No part of these lesson guides shall be reproduced in any form

without a written permission from the Bureau of Elementary Education, Department ofEducation.

The Mathematics Writing Committee

GRADE 5

Region 3

Nelia D. Bamba PampangaMagdalena P. Garcia Angeles City

Region 4

Gundalina C. Gonzales BatangasGerlie Ilagan QuezonConsuelo Caringal Batangas

National Capital Region (NCR)

Emma S. Makasiray Pasig/San JuanEster A. Santiago ValenzuelaMilagros Juakay Pasig/San JuanLucia Almazan ManilaJulie La Guardia Valenzuela

Bureau of Elementary Education (BEE)

Federico L. ReynoNoemi B. Aguilar

Ateneo de Manila University

Grace Uy

Support Staff

Ferdinand S. BergadoMa. Cristina C. CapellanEmilene Judith S. SisonJulius Peter M. SamuldeRoy L. ConcepcionMyrna D. LatozaEric S. de Guia Illustrator

Consultants

Fr. Bienvenido F. Nebres, SJ President,Ateneo de Manila University

Ms. Carmela C. Oracion Principal,Ateneo de Manila UniversityHigh School

Project Staff

Teresita G. Inciong Director IVMerlita A. Nolido Chief, Curriculum Development Division

Mirla R. Olores Asst. Chief, Curriculum Development DivisionVirginia T. Fernandez Project Coordinator

EXECUTIVE COMMITTEE

Edilberto C. de Jesus Secretary, Department of EducationJuan Miguel M. Luz Undersecretary for Finance and Administration

Fe A. Hidalgo Undersecretary for Programs and Projects

Printed in the Philippines.ISBN 971-92775-4-8


3/371

iii

TABLE OF CONTENTS

Introduction............................................................................................................................. viiMatrix .................................................................................................................................. vii-xviii

I. WHOLE NUMBERS

A. Comprehension of Whole Numbers

Reading and Writing Numbers through Billions .......................................................... 1Properties of Addition ................................................................................................ 4Properties of Multiplication ......................................................................................... 5Rounding Numbers ................................................................................................... 9Adding and Subtracting Large Numbers .................................................................... 12Multiplying Whole Numbers ....................................................................................... 16Dividing Whole Numbers ........................................................................................... 17One-Step Word Problems .......................................................................................... 20

Two to Three-Step Word Problems ............................................................................ 23Odd and Even Numbers ............................................................................................ 25Greatest Common Factors (GCF) of Given Numbers ................................................. 27Prime and Composite Numbers ................................................................................. 31Prime Factors of a Number ........................................................................................ 34Multiples of a Given Number...................................................................................... 37Least Common Multiple (LCM) of a Set of Numbers .................................................. 41Divisibility Rules

2, 5 and 10 .................................................................................................... 44 3, 6 and 9 ..................................................................................................... 47 Classifying Numbers as Divisible by 2, 3, 4, 5, 6, 9 and 10 ............................ 50 Classifying Numbers as Divisible by 2, 3, 4, 5, 6, 9 and 10 ............................ 52

II. RATIONAL NUMBERS

A. Comprehension of Fractions

Changing Dissimilar Fractions to Similar Fractions ..................................................... 54Equal Fractions ......................................................................................................... 58Changing Dissimilar Fractions to Lower/Higher Terms (LCM/GCF)............................. 62Estimating Fractions Close to 0, or 1 ...................................................................... 67

B. Addition

Adding Similar Fractions ............................................................................................ 71Visualizing Addition of Dissimilar Fractions ................................................................ 76Adding Dissimilar Fractions ....................................................................................... 81Adding Dissimilar Fractions and Whole Numbers ....................................................... 85Adding Whole Numbers and Mixed Forms ................................................................. 89Adding Dissimilar Fractions and Mixed Forms ............................................................ 93Adding Mixed Forms .................................................................................................. 96Estimating Sums of Fractions .................................................................................... 100Adding Mentally Similar Fractions .............................................................................. 103Solving Problems ...................................................................................................... 106


4/371

iv

C. Subtraction

Visualizing Subtraction of Fractions ........................................................................... 111Subtracting Whole Numbers from Mixed Forms ......................................................... 115Subtracting Mixed Forms (Similar Denominators) ...................................................... 118Subtracting Fractions from Whole Numbers ............................................................... 121Subtracting Fractions from Mixed Numbers ............................................................... 125Subtracting Mixed Number from Whole Numbers ....................................................... 130Visualizing Subtraction of Dissimilar Fractions ........................................................... 134Subtracting Dissimilar Fractions ................................................................................. 138Subtracting Dissimilar Fractions from Mixed Forms .................................................... 141Subtracting Mixed Forms ........................................................................................... 146One-Step Word Problems .......................................................................................... 151Two-Step Word Problems .......................................................................................... 155

D. Multiplication

Visualizing Multiplication of Fractions ......................................................................... 159Fractional Part of a Number ....................................................................................... 164Translating Expressions into Equations ..................................................................... 167

Multiplying Fractions By Fractions .................................................................................................. 171 By Whole Numbers ....................................................................................... 174 By Mixed Forms ............................................................................................ 177

Multiplying Mixed Forms ............................................................................................ 182Solving Problems ...................................................................................................... 186

E. Ratio and Proportion

Comparing and Writing Ratios ................................................................................... 190Ratios in Lowest Terms ............................................................................................. 194Equal Ratios .............................................................................................................. 196Ratio and Proportion .................................................................................................. 200

Missing Term in a Proportion ..................................................................................... 204

F. Decimals

Renaming in Decimal Form Fractions Whose Denominatorsare Powers of 10 ........................................................................................... 207

Place Value of Decimal Numbers .............................................................................. 211Reading and Writing Decimals through Thousandths ................................................. 213Rounding Decimals ................................................................................................... 217

G. Addition and Subtraction of Decimals

Adding Decimals ....................................................................................................... 219

Subtracting Decimals ................................................................................................. 221Adding Mixed Decimals with Regrouping ................................................................... 223Subtracting Mixed Decimals with Regrouping ............................................................ 227Solving Problems ...................................................................................................... 230Solving Two-Step Word Problems ............................................................................. 232


5/371

v

H. Multiplication of Decimals

Visualizing Multiplication of Decimals ......................................................................... 235Multiplying:

Tenths by Tenths .......................................................................................... 238 Hundredths by Tenths and Vice Versa .......................................................... 241

Mixed Decimals by Whole Numbers .............................................................. 243 Mixed Decimals by Mixed Decimals .............................................................. 246 Decimals by 10 and 100 ................................................................................ 250 Decimals Mentally ......................................................................................... 252

Solving Problems ...................................................................................................... 255

I. Division of Decimals

Visualizing Division of Decimals Using Models ........................................................... 258Dividing Decimals

By Whole Numbers ....................................................................................... 261 By Decimals through Hundredths .................................................................. 264

Solving Problems ...................................................................................................... 268

J. Percent

Visualizing Percent .................................................................................................... 270Relationship between Fractions, Ratio and Percent ................................................... 273Relationship between Percent and Decimal ............................................................... 277Relating Fractions, Ratios, Decimals and Percents .................................................... 280Meaning of Elements used in Solving Percentage Problems ...................................... 283Determining the Percentage of a Number .................................................................. 288

III. GEOMETRY

Visualizing Polygons .................................................................................................. 292Five or More Sided Polygons ..................................................................................... 295Visualizing and Identifying Congruent Polygons ......................................................... 297

IV. MEASUREMENT

A. Circumference of a Circle

Formula for Finding the Distance Around a Circle ...................................................... 301Circumference of a Circle .......................................................................................... 304Solving Problems involving Circumference Measure .................................................. 307

B. Area

Area of Parallelogram ................................................................................................ 309

Area of Trapezoid ...................................................................................................... 313Area of a Circle ......................................................................................................... 317Solving Problems ...................................................................................................... 320


6/371

vi

C. Volume

Unit of Measure Used for Measuring Volumeof Cubes and Rectangular Prism ................................................................... 323

Converting One Cubic Unit of Measure to Larger/Smaller Unit ................................... 325Counting Cubes to Find Volume of Cubes/Rectangular Prism .................................... 328Solving Problems ..................................................................................................... 332

D. Temperature Measure

Parts of a Thermometer ............................................................................................. 334Reading a Thermometer ............................................................................................ 336Solving Problems ...................................................................................................... 339

V. GRAPHS

A. Line Graph

Reading and Interpreting Data Presented in a Line Graph ......................................... 342Constructing a Line Graph ......................................................................................... 347

Finding the Average of Data Presented in a Line Graph ............................................. 350


7/371

vii

I N T R O D U C T I O N

The Lesson Guides in Elementary Mathematics were

developed by the Department of Education through the Bureau of

Elementary Education in coordination with the Ateneo de Manila

University. These resource materials have been purposely

prepared to help improve the mathematics instruction in the

elementary grades. These provide integration of values and life

skills using different teaching strategies for an interactive

teaching/learning process. Multiple intelligences techniques like

games, puzzles, songs, etc. are also integrated in each lesson;

hence, learning Mathematics becomes fun and enjoyable.

The skills are consistent with the Basic Education

Curriculum (BEC)/Philippine Elementary Learning Competencies

(PELC). These should be used by the teachers as a guide in their

day-to-day teaching plans.


8/371

viii

MATRIX IN ELEMENTARY MATHEMATICSGrade V

List of Competencies Values Integrated Strategies UsedMultiple Intelligence

Techniques

I. WHOLE NUMBERSA. Comprehension of

Whole Numbers1. Place Value Alertness, Accuracy Working back, Games,

Concept developmentNumbers, Movements,Cooperative groups

2. Properties of WholeNumbers

Addition Alertness, Speed Working back, Game Cooperative groups,Manipulative

Multiplication Cooperation, Activeparticipation,

Alertness

Concept development,Game

Manipulative

3. Rounding numbers Concern for others Modeling, Skilldevelopment

Manipulative, Charts

4. Operations of WholeNumbers: Adding and

SubtractingNeatness Flowchart, Concept

developmentPuzzles, Charts

Multiply WholeNumbers

Patience Concept development Numbers

Dividing WholeNumbers

Speed and accuracy Concept development,Modeling, Game

Investigation, Chart,Cooperative groups

5. Problem SolvingInvolving LargeNumbers: 1-step and2- to 3-step

Alertness, Accuracy,Cooperation

Simplifying theproblem, Game

Reading

6. Subset of WholeNumbers

6.1 Differentiate odd from

even numbers

Alertness Looking for patterns Numbers, Games, Chart

6.2 Give the commonfactors of givennumbers

Cooperation Listing method/Makingan organized list

Reading, Speaking,Writing, Numbers, Charts/Tables, Games,Simulation

6.3 Identify prime andcomposite numbers

Humility Concept development,Modeling

Games, Hands-onactivities, Reading,Speaking, Writing

6.4 Find prime factors ofa number

Alertness Listing, Tables, Makingan organized list

Numbers, Reading,Speaking, Writing,Cooperative groups,Hands-on activities

6.5 Show multiples of agiven number by 10,100

Willingness to joingroup activities

Listing, Tables Games, Numbers, Hands-on activities, Reading,Speaking, Writing

6.6 Find the leastcommon multiple ofa set of numbers

Cooperation Listing, Conceptdevelopment

Games, Hands-onactivities

Active participation Listing, Tables Numbers, Reading,Speaking, Writing,Games, Simulation, Logic

6.7 Tell when a numberis divisible byanother number(Divisibility Rules) Active participation

Appreciation for theuse of divisibility

Looking for patterns Games, Numbers,Reading, Speaking,Writing, Simulation, Logic


9/371

ix


Techniques

Rules in real lifesituations, Teamwork,

Sportsmanship

Tables/Listing Games, Charts, Reading,Speaking, Writing, Log

II. RATIONAL

NUMBERSA. Comprehension of

Fraction

1. Change dissimilarfractions to similarfractions

Helpfulness, Activeparticipation in class

activities

Concept development,Drawing, Modeling

Cooperative groups,Writing, Speaking, Writing

1.1 Visualize changingdissimilar fractions tosimilar fractions

1.2 Identify equalfractions

Positive attitudeTowards sharing

Modeling, Conceptdevelopment

Cooperative groups,Manipulatives

1.2.1 Use cross productto determinewhether 2 fractions

are equal

Thoughtfulness Concept development,Modeling

Games, Reading,Cooperative groups,Writing, Speaking

1.3 Change fractions tolower/higher term(LCM/GCF)

Diligence Listing, Modeling,Concept development

Cooperative groups,Hands-on activities

2. Estimate fractions

close to 0, 21

, or 1

Sportsmanship Modeling, Listing Games, Cooperativegroups, Writing

B. Comprehension onAddition ofFraction

1. Add numbers in mixedforms with similar

and dissimilarfractions without andwith regrouping

1.1 Add two to foursimilar fractions

Proper care of onesbelongings

Concept development,Modeling, Drawingpictures

Cooperative groups,Drawing, Reading,Writing, Speaking, Hands-on activities

1.2 Visualize addition ofdissimilar fractions

Peace and harmony Modeling, Guess andcheck

Cooperative groups,Hands-on activities,Games

1.3 Add dissimilarfractions

Obedience Concept development,Modeling, Drawingpictures, Simplifyingthe problem

Cooperative groups,Drawing, Reading,Writing, Speaking,Movement, Manipulative

1.4 Add dissimilar

fractions and wholenumbers

Industry Modeling, Listing,

Game

Manipulative, Storytelling,

Cooperation groups

1.5 Add whole numberand mixed forms

Spending time wisely Game, Drawing,Diagram, Modeling

Painting, Cooperativegroups, Puzzles

1.6 Add mixed form anda dissimilar fraction

Thoughtfulness Modeling, Conceptdevelopment

Use of Diagrams, Hands-on activities, Cooperativegroups

1.7 Add mixed forms Recycling,Cooperation

Modeling, Acting out Numbers, Reading,Writing, Speaking,Cooperative groups


10/371

x


Techniques

1.8 Estimate sum

1.9 Add mentally twofractional units withsimilar denominators

Helpfulness Concept development Speaking, Hands-onactivities

2. Application of Additionof Fractions2.1 Solve word problems

involving addition ofsimilar and dissimilarfractions without orwith regrouping

Cooperation Modeling, Flowchart,Concept development

Cooperative groups,Diagram, Numbers,Reading, Writing,Speaking, Scientificmethod

2.1.1 Analyze the wordproblem

2.1.1.1 Tell: what is asked what is/are given the word clue the operation to be

used

2.1.2 Transform wordproblem into anumber sentence

2.1.3 Use the correctoperation

2.1.4 State the completeanswer

C. Comprehension onSubtraction ofFractions

1. Subtract fractions andmixed forms withcommon denominatorswithout and withregrouping

1.1 Visualize subtractionof fractions

Perseverance in oneswork

Drawing pictures,Modeling, Acting outthe problem

Drawing, Hands-onactivities, Bodilymovements

1.2 Subtract wholenumbers frommixed forms

Helping parents/elders Looking for patterns,Decoding the secretmessage

Reading, Writing,Speaking

1.3 Subtract mixednumbers frommixed numbers(with similar

fractions)

Thrift and economy Concept development,Modeling

Hands-on activities,Manipulative, Cooperativegroups

1.4 Subtract fractionsfrom wholenumbers

Sharing Games, Conceptdevelopment, Modeling

Games, Hands-onactivities, Cooperativegroups

1.5 Subtract fractionsfrom mixednumbers

Love and concern Modeling, Acting outthe problem

Diagram, Nature,Cooperative groups, Self-awareness activities

1.6 Subtract mixednumbers fromwhole numbers

Dignity of labor Concept development,Drawing pictures,Flowchart

Independent study,Cooperative groups,Singing


11/371

xi


Techniques

2. Subtract DissimilarFractions

Cooperation Games, Modeling,Acting out the problem

Games, Cooperativegroups, Manipulative

2.1 Visualize subtractionof dissimilarfractions

Sharing Concept development,Drawing pictures

Games, Cooperativegroups, Manipulative

2.2 Subtract fractionsfrom mixednumbers

Love and concern Modeling, Acting outthe problem

Diagram, Nature,Cooperative groups, Self-awareness activities

2.3 Subtract mixednumbers frommixed numbers

Sharing onesblessings

Modeling, Conceptdevelopment


3. Subtract mentallysimilar fractions

4. Application ofSubtraction ofFractions

4.1 Solve word probleminvolvingsubtraction of

fractions

Positive attitudetowards body

exercise, Alertness

Drawing pictures,Cooperative learning

Cooperative groups

4.1.1 Analyze wordproblems


used4.1.2 Transform the word

problem into anumber sentence



5. Application of Additionand Subtraction ofFractions

5.1 Solve 2-step wordproblems involvingaddition andsubtraction offraction

Spend ones moneywisely

Drawing/diagram,Modeling

Cooperative groups,Reading, Speaking,Writing, Hands-onactivities

D. Comprehension of

Multiplication ofFractions1. Multiply fractions bywhole number, mixedform by a fraction1.1 Visualizemultiplication of fractions

Cooperation Visualization, Modeling Diagram, Cooperativegroups, Manipulative

1.2 Find a fractional partof a number

Alertness, Activeparticipation

Concept development,Group contest,Simplifying theproblem

Manipulative, Drawings,Linguistics


12/371

xii


Techniques

1.2.1 Translate

expressions such as 21

of 32

of 61

1.3 Multiply1.3.1 fraction by anotherfraction

Sharing, Accuracy incomputation

Concept development Manipulative, Cooperativegroups

1.3.2 fraction by a wholenumber

Sharing Group games,Modeling, Drawinggraphs

Graphs, Speaking

1.3.3 mixed form by afraction

Wise buying andchoosing the right kind

of food

Concept development,Modeling

Cooperative groups,Speaking, Reading,Writing, Movements,Reporting

1.3.4 mixed form by amixed form

Positive attitudetowards work

Modeling, Using grids,Drawing picture

Speaking, Charts

2. Multiply mentally

fraction units3. Application ofmultiplication of fractions3.1 Solve word problemsinvolving multiplication offractions

Willingness to work Concept development Reading, Writing,Reporting


Sharing blessings withothers

Simplifying theproblem, Writingequation

Cooperative groups,Movements, Independentstudy


used

3.1.2 Transform the wordproblem into numbersentence3.1.3 Use the determinedoperations3.1.4 State the completeanswer4. Application ofMultiplication

E. Comprehension ofRatio and ProportionReducing ratios to lowest

terms

Love for Mother Earth Modeling, Use of

tables

Global themes, Charts

1. Express the ratio oftwo numbers1.1 Visualize the ratio oftwo given sets of objects

Appreciation,Cooperation

Modeling, Use oftables, Finding apattern

Tables, Self-awareness,Cooperative groups

1.2 Express the ratio oftwo numbers by usingeither colon (:) or afraction

Appreciation Use of tables, Conceptdevelopment



13/371

xiii


Techniques

2. Forms Proportion forNumbers

Cooperation Cooperative learning,Finding a pattern,Concept development

Cooperative groups

F. Comprehension ofDecimals1. Read and writedecimals throughthousandths

Awareness to currentissues

Drawing table, Chart,Looking for patterns

Manipulative, Tables,Charts

1.1 Rename in decimalform fraction whosedenominators are powersof 10

Accuracy, Alertness,Speed

Using Tables,Diagrams, Modeling,Simplifying theproblem

Reading, Speaking,Writing, Numbers

1.2 Give the place valueof each digit of a givendecimal

Accuracy, Orderliness Concept development Constructing charts,Reading, Speaking,Writing, Cooperativegroups, Individual study

2. Round decimals to thenearesttenths/hundredths/thousandths

Accuracy, Speed Concept development,Modeling, Discoveringa pattern

Body movement,Independent study,Speaking, Drawing

G. Comprehension ofAddition andSubtraction ofDecimals

Accuracy, Speed Concept development,Skill development

Reading, Speaking,Writing, Games

1. Add and subtractdecimals through

thousandths without andwith regrouping

Accuracy, Speed Game, Conceptdevelopment

Numbers

2. Add and subtractmixed decimals withregrouping

Accuracy Modeling, Conceptdevelopment, Actingout the problem

Cooperative groups,Hands-on activities,Speaking

Subtract mixeddecimals withregrouping

Accuracy Game, Conceptdevelopment

Charts, Cooperativegroups

Subtract mixeddecimals from wholenumbers

Dignity of labor Concept development,Drawing, Pictures,Flowchart

Independent study,Cooperative groups,Singing

3. Application of additionand subtraction ofdecimals3.1 Solve word problems

involving either additionor subtraction ofdecimals includingmoney

Accuracy, Speed,

Thoughtfulness, Thrift

Guess and check,

Educated guess,Simplifying theproblem

Reading, Speaking

3.2 Solve 2-step wordproblems involvingaddition and subtractionof decimals includingmoney

Appreciation Group games,Simplifying theproblem

Movements, Cooperativegroups


14/371

xiv


Techniques

H. Comprehension ofMultiplication ofDecimals1. Multiply mixeddecimals and whole

numbers1.1 Visualizemultiplication of decimalsusing models

Keep ones work andwork area neat and

clean

Modeling, Drawinggraphs

Cooperative groups,Graphs

1.2 Tenths by anothertenths

Appreciation of thebeauty of nature

Concept development,Modeling

Diagrams, Nature

1.3 Hundredths by tenthsand vice versa

Sharing Acting out the problem,Looking for patterns

Diagrams

2. Generalize the step inmultiplying decimals3. Multiply mixeddecimals with tenths andhundredths by wholenumbers

Working well withothers

Games, Conceptdevelopment

Games, Hands-onactivities, Cooperativegroups

4. Multiply mixeddecimals by mixeddecimals with tenths andhundredths

Health consciousness,Accuracy

Game, Conceptdevelopment

Puzzles

5. Multiply decimals by10 and 100

Awareness Looking for patterns,Acting out the problem

Tables, Self-awarenessactivities

6. Multiply decimalsmentally by 0.1, 0.01,and 0.001

Helpfulness,Cooperation

Looking for patterns,Drawing tables

Tables, Cooperativegroups

7. Application ofMultiplication of Decimals7.1 Solve word problemsinvolving multiplication ofdecimals includingmoney

Accuracy, Spendingmoney wisely

Acting out the problem,Simplifying theproblem

Writing, Speaking, Simpleplay, Cooperative groups

I. Comprehension ofDivision of Decimals1. Divides decimalsthrough hundredths1.1 Visualize division ofdecimals using models

Cooperation Modeling, Acting outthe problem

Cooperative groups,Manipulative, Hands-onactivities, Reading,Writing

1.2 Divide decimals bywhole numbers

Health consciousness Concept development,Modeling

Independent study,Reading, Writing,Speaking, Graphing

1.3 Divide decimals bydecimals throughhundredths2. Application of Divisionof Decimals2.1 Solve word problemsinvolving division ofdecimals

Wise spending Concept development,Simplifying theproblem

Independent study,Reading, Writing,Speaking, Diagrams



15/371

xv


Techniques

2.1.1.1 Tell:- what is asked- what is/are given- the word clue- the operation to be

used2.1.2 Transform the word




J. Comprehension ofPercent

1. Relate fractions/ratios,decimals and percent

1.1 Visualize themeaning of percent(%)

Cooperation,Appreciation for the

use of percent in real-life situations

Modeling, Drawingpictures, Conceptdevelopment

Drawing, Hands-onactivities, Manipulative,Cooperative groups

1.2 Give the relationship between

fractions/ratios andpercents (withvisual models)

Health consciousness,Showing concerns for

others

Concept development,Modeling, Makingtables

Collecting data, Scientificmethod, Music, Dancing,Body movements, Usingchart

between percentand decimal (withvisual models)

Cooperation Concept development,

Acting out the problem

Reading, Writing,

Speaking, Manipulative

among fractions/ratios, decimals andpercents

Honesty Acting out the problem,Modeling, Preparing atable

Skit and play, Hands-onactivities, Reading,Writing, Speaking,Drawing

III. GEOMETRYA. Comprehension of

Polygons1. Draws 3- to 4-sided

polygons1.1 Visualize polygons Work cooperatively in

a group, PatienceModeling, Drawingpictures, Acting out theproblem

Hands-on activities,Speaking, Drawing,Cooperative groups

1.2 Identifies kinds ofpolygons

1.3 Describes polygons2. Draws 5- or more-

sided polygons e.g.pentagon, hexagon,etc.

Cooperation Looking for patterns,Modeling, Drawingpictures

Nature, Drawing,Cooperative groups


16/371

xvi


Techniques

2.1.2 Transforms theword problem into anumber sentence

2.1.3 Uses the correctoperation

2.1.4 States the completeanswer

IV. MEASUREMENTA. Comprehension of

Area1. Finds the area of other

plane figures in squaremeters/centimeters

parallelograms trapezoids circles

2. Application ofMeasurement of Area

2.1 Solves wordproblems involvingarea of plane figures

2.1.1 Analyzes the wordproblem

Patience, Industry,Helpfulness

Modeling, Simplifyingthe problem, Writingequation

Reading, Writing,Speaking, Cooperativegroups, Diagrams

3. Draws congruent andsimilar polygons

3.1 Visualizescongruence/ similarityof polygons

Willingness to doassigned task

3.2 Identifies congruent/similar polygons

B. Comprehension ofCircumference ofCircle

1. Finds thecircumference of acircle in centimeter/meter

1.1 Derives a formula forfinding the distancearound circle

Accuracy Concept development,Acting out the problem,Modeling, Developingformula and writing

equation

Movements, Cooperativegroups, Manipulative

2. Application of theConcept ofCircumference

2.1 Solves wordproblems involvingcircumferencemeasure

Creativity in doingthings

Simplifying theproblem

Cooperative groups,Reading, Writing,Speaking

2.1.1 Analyzes the wordproblem


17/371

xvii


Techniques

2.1.1.1 Tell:

what isasked

what is/aregiven

the word clue the operation

to be used2.1.2 Transform the word




C. Comprehension of

Volume1. Find the volume of acube/ rectangularprism

1.1 Tell the unit ofmeasure used formeasuring the volumeof cubes/ rectangularprism

Accuracy Concept development Game, Manipulative,Hands-on activities,Reading, Writing,Speaking

1.2 Convert one cubicunit of measure to alarger or smaller unit

Active participation Listing Game, Numbers,Cooperative groups,Reading, Writing,Speaking

1.3 Derive a formula forfinding the volume of

cube/rectangular prism

Appreciation ofapplication of volume

in daily life situations

Develop formula andwrite equation

Game, Manipulative,Hands-on activities,

Reading, Writing,Speaking, Diagrams

2. Application ofMeasurement ofVolume

2.1 Solve word problemsinvolving measurementof volume

Sharing Guess and check,Modeling

Scientific method, Nature


2.1.1.1 Tell:

what isasked

what is/aregiven

the word clue the operation

to be used2.1.2 Transform the word




18/371

xviii


Techniques


D. Comprehension ofTemperatureMeasure

1. Give body/weathertemperature usingdegree Celsius

1.1 Identify the parts of athermometer

Sportsmanship Modeling, Groupgames

Reading, Writing,Speaking, Cooperativegroups

1.2 Read a thermometer Cooperation Concept development,Modeling, Groupgames

Cooperative groups,Movements, Reading,Writing, Speaking

2. Application ofTemperature Measure

2.1 Solve word problem

involving body/weathertemperature

Accuracy Visualization, Acting

out the problem

Nature, Scientific method

V. GraphsA. Comprehension of

Graphs1. Read/Interpret data

presented in a linegraph

Proper nutrition Drawing graphs Graphs, Self-awarenessactivities

2. Read a line graph3. Construct a line graph Cooperation Graphs, Tables Graphs, Cooperative

groups3.1 Organize data

presented in a linegraph

3.2 Find the average ofdata presented in aline graph

Cooperation Graphs, Tables Cooperative groups,Reading, Writing,Speaking, Games,Numbers, Graphs


19/371

1

Reading and Writing Numbers through Billions

I. Learning Objectives

Cognitive: 1. Give the place value of each digit in a 6- or more digit number

2. Read and write numbers through billions in figures and in words correctlyPsychomotor: Write numbers through billions in figures and in wordsAffective: Observe accuracy in reading and writing numbers through billions in figures and

in words

II. Learning Content

Skill: Reading and writing numbers through billions in figures and in wordsReference: BEC-PELC I.A.1Materials: place value chart, number cardsValue: Alertness, Accuracy

III. Learning Experiences

A. Preparatory Activities

1. Drill

Writing Numbers in Expanded Form to Standard Form

Strategy 1 Think and Share

Materials: expanded form of numbers written in reusablecard board like boxes of powdered soap

Mechanics:a. Distribute 2 copies of a number in expanded form to a boy and a girl.

b. Let the two write the standard form of the number one on top of the other on the board.c. The purpose of the game is to easily compare the places and digits of the standard formof the number.

d. Have volunteers read the first number, give the place value of each digit and the value ofeach digit.

e. Then have them give the place value and the value of each digit in the second number.f. The game continues until all the five pairs of numbers are written on the board.

Strategy 2 Forming Numbers (Game)

Materials: Number cards with numbers 0-9 written on reusablematerials like boxes of milk, powdered detergent, etc.

Mechanics:a. One group of 10 boys and 1 group of 10 girls will be given number cards 0-9.

b. As the teacher says a number, the boys and the girls groups will form the said numberas fast as they could by standing in front of the class.

c. The group that is able to form the correct number first gets the point.d. The game will go on until all the numbers prepared by the teacher have been dictated.e. The group with the highest points wins.

2. Review

Reading smaller group of numbers written on reusable materials


20/371

2

B. Developmental Activities

1. Presentation

Strategy 1: Problem Opener

The total student population in the Philippines according to the Philippine Yearbook1999 is sixteen million, three hundred nine thousand, five hundred fifty-six.

Ask the following questions:a. How is this number written in numerals?b. How are the digits grouped?c. Where do we start grouping the number by 3s?d. How are the three-digit number groups separated from the other number groups?e. Where does the value of each period as well as each digit in the periods depend?f. What is the role of zero in a number?

Strategy 2: Picking Flowers Relay (Game)

Materials: Paper flowers clipped on a cartolina tree

Mechanics:a. Divide the class into 2 groups 10 boys and 10 girls.b. Teacher posts a tree on the board with flowers having numbers on them.c. As the teacher says a number, the first set of participants rushes to the board to pick the

flowers corresponding to the dictated number.d. The participant who gets the right flower keeps the flower and gets the point for his/her

group.e. The game goes on until all the flowers are picked. The group that has the most flowers

wins.

Ask:a. What guided you to get the right number?b. How many periods do you see in hundred, thousand, million, and a billion?

c. What should you remember in writing and reading numbers?

Strategy 3: Posting a Place Value Chart (Concept Development)

Teacher dictates numbers and let pupils put number cards on the place value chart torepresent the dictated number. The activity is done until all the chart is filled with the dictatednumbers. Let the pupils read the numbers on the place value chart.

Ask:a. How were you able to read the numbers?b. What is the largest period in a four-period numeral?c. What do you place when one of the place values is not mentioned in a period?d. What do you call zero then?

2. Generalization

How many periods are there in a billion?What are the periods in a billion?Where do you start reading numbers?How is each period separated from the other?What is placed after each period when writing numbers in words?


21/371

3

C. Application

1. Write the following numbers in words:

a) 2 750 000b) 3 726 513

c) 43 000 210d) 412 876 010e) 234 126 143f) 1 046 287 130g) 961 428 157 380h) 2 704 680 415i) 3 456 839 701

j) 258 400 007 130

2. Write the numerals of the following:a. three million seven hundred twenty three thousand, one hundred twentyb. five hundred thirty five million two hundred forty fourc. four thousand three

d. six hundred eighty thousand eight hundred twoe. eight hundred forty seven million three hundred fifty six thousand four hundred fifteen

IV. Evaluation

A. Write each number in standard form.

1) 75 billion, 84 million, 26 thousand2) 149 billion, 400 thousand, twelve3) 4 billion, 180 thousand4) thirty-five million, ten thousand5) sixty billion6) twenty billion, five million, five

B. Write the value of the underlined digit in each number.

1) 3 100 423 0002) 9 287 6003) 412 876 010 0514) 17 386 001 0005) 234 126 143

V. Assignment

A. Write the following numerals in words.1) 436 510 2102) 2 004 7163) 14 287 000

4) 8 286 000 4505) 3 012 428 000

B. In the numeral 927 814 760 537, write each digit in the proper place according to value.a. thousands g. hundred millions

b. ten millions h. hundred billions

c. billions i. hundred thousands

d. hundreds j. ten billions

e. ones k. millions

f. ten thousands l. tens


22/371

4

Properties of Addition


Cognitive: 1. Identify the properties of addition used in an equation2. Add numbers using the properties

Psychomotor: Write the sum of a given set of numbersAffective: 1. Appreciate the use of properties of addition for quicker computation

2. Work quickly but accurately


Skill: Using the properties of addition to help find the sumReference: BEC-PELC I.A.2.aMaterials: Flash cardsValue: 1. Appreciation for the use of the properties of addition

2. Working quickly but accurately



Materials: set of flash cards with 3-6 digit addends that are compatible

1. Teacher prepares flash cards with numbers that are compatible where properties ofaddition are easy to use.

Example:

2. Teacher divides the class into 3 groups. Teacher shows the class a card and asks the pupilsto solve mentally as fast as they can. Teacher may give time limit to answer (i.e. 10-15seconds) depending on how difficult/easy the items are. No other means of computation is

allowed except mental computations.3. Team with the most points wins.


1. Presentation

a) Teacher posts several cards on the board to be used as example.b) Ask from pupils the ways of finding the sum of a set of numbers quickly.

Example: 0 + 5 =, 4 + 6 = 6 + 4, (12 + 7) + 8 =, 12 + (7 + 8)c) Teacher probes if such techniques are possible. Does changing the order of adding

change the sum? Verify by actual adding. 12 + 15 = 27 or 19 + 8 = 27, 0 + 5 = 5d) Elicit reason why the strategies mentioned by students were commutative, associative

and identity.e) Define and illustrate each. Mention that zero is the identity in addition.f) Provide more examples.g) Cooperative Learning Activity: Rally Table

1) Group class into groups of 4. Provide each group with worksheet with 10 items.2) Pupil 1 answers question 1 mentally.3) After time limit, teacher rings the bell and the paper is passed on pupil #2 of each

group.4) Pupil #2 answers question 2.5) This pattern continues with person #1 answering question 5.

1+5+19+15 or

12+ 7

8


23/371

5

6) Check answers.7) Have group discuss incorrect items and how these could be answered correctly.8) Value Infusion: Who was able to benefit from knowing the properties? How did they

help you in computing for the sum?

2. Generalization

What are the properties of addition?What is the commutative property of addition?Associative property? Identity property?

C. Application

Name the properties used.

1) (7 + 8) + 2 = 7 + (8 + 2) ______2) 3 + 9 = 9 + 3 ______3) 14 + 0 = 14 ______4) 4 + (7 + 6 ) = (4 + 6) + 7 ______5) (5 + 3) + 7 = 5 + (3 + 7) ______6) (5 + 1) + 2 = 5 + (2 + 1) ______

IV. Evaluation

Find each missing addend. Name the properties you used.

1) (12 + 3) + =+ (3 + 5)3) 27 += 275) (32 +) + 8 = 32 + (8 + 7)

2) 35 + 0 += 35 + 9 + 04) (4 +) + 16 = 4 + (16 + 12)6) (2 + 19) += (2 + 9) + 19

V. Assignment

Use the properties to complete each sentence.

1) 24 + 12 + 6 =

3) 65 + 20 + 115 =5) 0 + 574 =7) 0 + 45 + 7 =9) 479 + 0 =

2) 33 + 10 + 7 =

4) 15 + 12 + 9 =6) 30 + 20 + 15 =8) 16 + 30 + 14 =10) 25 + 35 + 10 =

Properties of Multiplication


Cognitive: 1. Identify the properties of multiplication2. Find the product using the properties of multiplication

Psychomotor: Write the equation and the answer illustrating the properties of multiplication

Affective: 1. Cooperate actively with the group2. Be alert in every activity


Skill: Identifying and showing the properties of multiplicationReference: BEC-PELC I.A.2.bMaterials: objects or bottle capsValue: Cooperation, active participation and alertness


24/371

6



Name the properties used.1) (5 + 7) + 4 = 5 + (7 + 4)2) 6 + 3 = 3 + 6

3) 12 + 0 = 124) 2 + (5 + 3) = 2 + (3 + 5)5) (7 + 1) + 2 = 7 + (2 + 1)

Strategy 1: Place Value - Game

Materials: Flash cardsMechanics:a. Form dyads.b. Teacher flashes card like 426, 859, 206, 357c. Each dyad or each pair has only one answer sheet. One player writes the answer in number

one.d. The first player of each dyad passes the answer sheet to his/her partner who in turn answers

number two.e. This game continues up to the 10

thround.

f. Each dyad exchanges answer sheets for checking.g. The dyads or pairs with the most number of correct answers are winners. There maybe more

than one winner in this kind of game.


1. Presentation

Strategy 1: Using concrete object

Materials: Counter/bottle capsMechanics:a. Distribute 24 counters to each pair.b. Partner 1 uses counters to show a 6 by 2 array. Partner 2 shows a 2 by 6 array.c. Partners discuss similarities and differences in arrays.d. They write multiplication sentence for each array.

(6 x 2 = 12, 2 x 6 = 12)e. Repeat activity for these arrays:

3 by 4, 4 by 3; 2 by 4, 4 by 2 (5 10 min.)f. Teacher asks what pupils say about the product. (The order of the factors does not

change the product).g. This is the Commutative Property of Multiplication.

Strategy 2: Whole class activity

Mechanics:a. Divide the class into 6 groups. Two groups will be doing the same equations.b. Teacher distributes equation cards to each group for them to solve.

For example:Group 1 and 2 32 x 1 = N

1 x 32 = NGroup 3 and 4 29 x 0 = N

0 x 29 = N


25/371

7

Group 5 & 6 6 x (4 + 5) = N6 x (4 + 5) = (6 x 4) + (6 x 5)6 x _____ = _____ + _____

________ = ________

c. Every group works on the equation.d. Each group reports.

The groups should come up with these:1 and 2 The product of any number and one is the same number (IdentityProperty)3 and 4 The product of any number and zero (0) is zero (0). (Zero Property)5 and 6 If one factor is a sum, multiplying before adding does not change the product.

e. Why do some groups finish their work earlier than others?f. How did you participate in the activities?

Strategy 3: Show-Me Game

Mechanics:a. Each pupil has his/her own show-me card.b. Teacher flashes equations like: 15 x 0 = 0

7 x (5 + 4) = (7 x 5) + (7 x 4) 8 x 6 = 6 x 8,

8 x (4 x 7) = (8 x 4) x 7 29 x 1 = 29

c. Each pupil writes the property illustrated in his/her own card.d. As the teacher shows the signal, pupils raise their show-me cards.e. This continues up to the 10th round.

2. Generalization

The properties of multiplication are: Commutative Property

The order of the factors does not change the product. Associative Property

The way the factors are grouped does not change the product or a change in thegrouping of the factors does not affect the product.

Identity PropertyThe product of any number and one is that number.

Zero PropertyThe product of any number and zero is 0.

Distributive Property of Multiplication over AdditionIf one factor is a sum, multiplying before adding does not change the product.

IV. Evaluation

A. Identify the property of multiplication shown in each number.

1) 4 761 x 0 = 0 2) 8 x (4 x 9) = (8 x 4) x 93) 8 x 27 = 27 x 8 4) 4 x (3 + 6) = (4 x 3) + (4 x 6)5) 956 x 1 = 956 6) 9 x 14 = 14 x 97) 248 x 0 = 0 8) 25 x 1 = 259) 6 x (8 x 10) = (6 x 8) x 10 10) 6 x (7 + 3) = (6 x 7) + (6 x 3)


26/371

8

B. Write true or false. If true, identify the property of multiplication illustrated.

1) 8 x 4 = 4 x 83) (3 x 4) + (4 x 5) = (3 x 4) x 55) 7 x (4 + 2) = ( x 4) + 27) (8 + 2) x 3 = (8 x 3) + (2 x 3)

9) 10 x 96 = 90 x 10 + 6

2) 5 x (2 x 6) = (5 x 2) x (6 x 5)4) 0 x 5 = 06) 7 x 82 = (7 x 80) + (7 x 2)8) 457 x 0 = 0

10) 9 x (6 + 4) = (9 x 6) + (9 x 4)

C. Use the distributive property to find the product.

1) 8 x (40 + 3) = ( __ x __) + (__ x __)= ________ + ________

= __________

2) 7 x (8 + 3) = (__ x __) + (__ x __)= _________ + ________= ___________

3) 4 x (20 + 6) = (__ x __) + (__ x __)= ________ + ________

= ___________

4) 6 x (2 + 3) = (6 x __) + (6 x __)= _______ + ________= _________

5) 5 x (4 + 3) = (5 x __) + (5 x __)= ________ + _______= ___________

D. Solve for the product.

1) 3 x (5 x 6) = (3 x 5) x 63 x ____ = _____ x _____

______ = _______

2) 6 x (30+ 5) = (__ x __) + (__ x __)= ________ + _________= _________

3) 9 x 8 = ___ x 9____ = _____

4) 8 x (7 x 5) = (8 x 7) x 5___ x ___ = ___ x ___________ = ________

5) 4 x (9 + 7) = (____) + (____)

= _____ + ______= ________

V. Assignment

Solve for the product then identify the property of multiplication illustrated.

1) 9 x (6 + 5) = ____________3) 2 657 x 1 = _____________5) 0 x 4784 = _____________

2) 4 x (10 x 8) = (4 x 10) x 8 __________4) 8 x (6 + 4) = ___________


27/371

9

Rounding Numbers


Cognitive: Round off numbers to the nearest indicated place valuePsychomotor: Write numbers rounded to the indicated place value

Affective: 1. Wait for ones turn in a game2. Demonstrate consciousness of too much food wastage3. Appreciate use of rounding off numbers in real life situations


Skills: Rounding numbers to the nearest tens, hundreds, thousands, ten thousands etc.Reference: BEC-PELC I.A.3Materials: Flash cards, cutouts, number line, number cardsValue: 1. Appreciation for use of rounding off numbers in real-life situations

2. Consciousness of too much food wastage



1. Drill

Drill on Reading Numbers Through Billions

Strategy 1: Game - Catching Fish

Materials: picture of an aquarium with cutouts of fishes, numbers through billionsare written in cutouts of different kinds of fish

Mechanics:a. Teacher divides class into two groups.

b. Draw lots to decide who will be the first player.c. The first player catches fish by getting one cutout and reading the numeral correctly.Reading the numeral accurately means one point for the group.

d. The second player comes from the other group.e. The two groups take their turns.f. The game continues up to the 10

th round.

g. The group with the most number of points wins.

Strategy 2: Group Game

Materials: flash cardsMechanics:a. Teacher divides the class into 4 teams.

b. Flash a number, for example, 27 000 426 598.c. The first pupil from each team reads the numeral. The rest of the team members take

turns.d. Team gets a point if the answer is correct.e. The game continues until a team gains 10 points. This team is announced the winner.


28/371

10

2. Review

Strategy 1: Show Me GameMaterials: Show-Me CardsMechanics:a. Each pupil has his/her own Show-Me Card.b. Teacher dictates a numeral through billions, for example:

fifty six billion, nine million, eight billionc. Each pupil writes the number on Show-Me Cards.d. When the teacher gives the signal, everybody raises his/her card.e. Every pupil makes a record of his/her score. (This develops honesty, a very important

value.)f. This activity continues up to the 10

thround.

3. Motivation

Problem OpenerThe Cruz family is preparing food for their 187 expected guests to their town fiesta.

For how many people, to the nearest hundred, should they prepare for?What is given? What is being asked? How do we solve the problem?


1. Presentation

Strategy 1: Use the number line (Skill Development)

Mechanics:a. Draw a number line on the board. Elicit from the pupils the whole number of points that

are needed according to the problem, (nearest hundreds) namely 100 and 200.b. Have pupils plot 187. Lead pupils to answer the problem by asking: Which hundred is

187 closer to?c. Provide another number. What if we are expecting 125 guests instead? Follow the same

process.

d. Elicit from pupils which number would round up to 200 (150-199). Mention that when weread the halfway mark, we round up.

e. Generalize the rule for rounding off based on pupils observations.f. Provide more examples using different place values.

Strategy 2: Using members of the classInstead of using the number line, teacher may use the pupils instead.a. Have two pupil hold cards bearing 100 and 200 (based on the problem)b. Call on another pupils to hold 187 and ask him to find his place between the two other

pupils.c. Teacher asks: To which hundred is 187 closer to?d. Provide more examples: 125, 145, 168e. Generalize the rule by asking which would be closer to 100 and which ones will be closer

to 200. Lead pupils into looking at the tens digit.f. What if we want to find the nearest tens of 187? (180 and 190)g. Provide more examples using different place values.

Value Infusion1. If you were preparing for fiesta, will it be better to prepare more or less food than the

guests expected? What would happen if you prepare too much food? Too less food?2. Lead also the pupils in appreciating the use of rounding off/estimation in daily life.

Ask question like: When is it better to round up in real-life situations? What situationswould require you to round down instead?


29/371

11

Strategy 3

Materials: Number line, ChipsMechanics:a. Draw a number line on the board.b. Show the numbers between 700 and 800.c. Draw a special point at 750.d. Teacher writes numbers between 700 and 800 on ten chips.e. The pupils play with a partner. Alternately, they take turn in turning the chips over,

rounding the number of hundreds and placing the chips on the proper side of 750 on theline.

2. Generalization

In rounding off numbers to the nearest tens, look at the digit at the right of the number tobe rounded. If it is 1,2,3,4 retain the digit and replace other digits that follow with zeros. If itis 5,6,7,8 , or 9, add one to the digit to be rounded and with zeros after it.

C. Application

1. Name the place value where the numbers are rounded.a) 890c) 456 000e) 580 000 000

b) 700 000 000d) 980 000 000

2. Give the least number that can be rounded off to the following place values.a) tensc) thousandse) hundreds

b) millionsd) hundred thousands

3. Give the greatest number that can be rounded off to the indicated place values.a) hundred thousandsc) ten thousands

e) tens

b) hundredsd) ten millions

IV. Evaluation

A. Round each number to the nearest.

Tens Hundreds Thousands

1) 2 368

2) 5 059

3) 6 542

4) 18 565

5) 57 558

B. Round the numbers to the nearest.

Ten thousands Hundred thousands

1) 4 315 652

2) 7 354 754

3) 6 812 563

4) 9 451 245

5) 3 645 157


30/371

12

C. Round off the following numbers to the indicated place value.1) 865 to the nearest hundreds2) 597 644 to the nearest ten thousands3) 715 to the nearest ten pesos4) 50 138 to the nearest hundred pesos5) 865 207 to the nearest hundred thousands

D. Answer the following questions:1. To what place value is 670 000 rounded off?2. What is the greatest number that can be rounded off to the nearest millions?3. Give the least number that can be rounded to the nearest ten thousands.4. Give the greatest number that can be rounded to the nearest thousands.

V. Assignment

A. List down at least 2 numbers that can be rounded off to the nearest:1. hundreds3. thousands

2. ten thousands4. hundred thousands

5. hundred millions7. billions

6. millions8. ten millions

Adding and Subtracting Large Numbers


Cognitive: 1. Review the process of adding and solving large numbers with and withoutregrouping2. Solve word problems involving addition and subtraction of whole numbers

Psychomotor: Write numbers in column properlyAffective: 1. Persevere in working with large numbers

2. Work cooperatively with a partner or group


Skill: Reviewing addition and subtraction of large numbersAddition and Subtraction of large numbers with and without regrouping

Reference: BEC-PELC I.A.4.aMaterials: cards, chart, cartolina, strips of paperValue: Perseverance, cooperation



1. Drill

Ask the pupils to give the sum and difference of the numbers found on each slice of the pie.

20 4018 35

70 20 1532

22 1650 60


31/371

13

2. Review

a. Pupils will be grouped. Each group will be given activity sheets which they will work on.b. The following exercises are written on the activity sheets.

Identify the property of addition and fill in each blank with the correct answer.1) 56 + 34 = _____ + 56 = ______

2) 569 + 0 = _____3) (5+9) + 6 = 5 + ( _ + 6) + ______4) ( __ + 2) + 16 = 8 + (2 + 16) = _______5) (32 + 8) + ___ = 32 + (8 + 9) = ______

c. The first group to finish will be the winner.How did you work with your group?

3. Motivation

Show a lotto card.Let the pupils identify the use of the card.What comes to your mind when you hear or see this card?

Can you imagine the amount of money that you can get if you own the winning lotto numbercombination?


1. Presentation

Strategy: Problem Opener

Miss Nims poultry farm produced 46 578 eggs in 2000 and 51 254 eggs in 2001.How many eggs were produced in two years? How many more eggs were produced in 2001than in 2000?

2. Analysis and Discussion

a. What is asked?b. What are the given facts?c. What operation will be used to answer the first question?d. Write the equation for the problem.

46 578 + 51 254 =e. Let the pupils identify the parts of the equation. (addends, sum)f. What are the steps in finding the sum of large numbers?

1) Write the addends in column. Ones under ones, tens under tens, hundreds underhundreds up to billions.(Prepare a place value chart. Let the pupils write the addends in appropriate column.)

2) Begin at the right, adding each figure and writing the sum underneath.What is the answer?The total number of eggs produced in two years, 97 832.a) What is the other question in our problem?b) (How many more eggs were produced in 2001 than in 2000.)c) What operation are we going to use to answer that question?d) What is the number sentence or equation?

57 254 - 46 578 =e) Name the parts of a subtraction equation. (Minuend, subtrahend, difference)f) Ask: What are the steps in subtracting large numbers with regrouping?


32/371

14

g) Teacher explains: We regroup or borrow from the digit to the left if the digit inthe minuend is smaller than the digit in the subtrahend.

h) Discuss how to check answers by performing the inverse operation.Learning exercise.Find the hidden message.Find the sum and difference of the given numbers. Write in the blanks the letter forthe answer in the code.

Message

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Code: A E N A I

943 899 724 40 008 921 147 925 107 85 106 730 12 886 825

A T E A M

1 403 899265

782 112 2214 418 256

7211 112 489

377318 024 218

M H L R R

2 984 259 69 518 805390

409 139 723 1 047 742893

257 691 311

1) 565 247+ 12 321 578

4) 834 578 264+ 569 321 001

7) 534 298 786+ 247 813 435

10) 15 264 578 294- 10 846 321 573

13) 569 246 321- 421 321 214

2) 574 234 678+ 538 254 699

5) 32 578 264- 29 594 005

8) 15 254 674 78+ 54 264 131 112

11) 674 578 246+ 269 321 478

14) 321 578 264- 281 569 478

3) 587 264 539- 269 240 321

6) 154 264 784- 69 158 054

9) 878 464 294- 469 324 571

12) 578 464 324+ 469 278 569

15) 789 265 578- 531 574 267

3. Generalization

How do we add/subtract large numbers with regrouping? Without regrouping?

C. Application

Do the indicated operation.1) 638 431 + 972 302 + 439 166 =2) 451 384 + 618 175 + 806 429 =3) 906 382 529 495 =4) 703 800 476 347 =5) 870 006 618 718 =


33/371

15

IV. Evaluation

A. Complete the Number Puzzle.

a b c d e

f

g

h

i

Across Down

a. Add 346 541 588 and a. From 88 340 864 625 subtract231 704 733 34 578 321 411.

f. The sum of 269 595 387 b. Take away 6 254 467 from 14 599 599.and 165 385 013

g. 39 567 434 399 + c. Find the difference between17 175 760 280 1 380 655 679 and 946 398 895

h. What is the total of 143 321 478 939and 113 026 788 519? d. Subtract 688 561 294 from 1 037 137 726

i. What is 299 749 123 increased by e. Deduct 7 934 567 from 9 377 915.187 894 091?

B. Solve the following correctly.

1. From 189 860 take away 56 7802. Find the difference between 864 466

508 and 792 648 8503. Find the difference between 162 488

462 and 87 498 624

4. Take 874 321 987 from 922 498 6745. Subtract 146 935 975 from 371 297 465

V. Assignment

A. Complete the chart. Write the sum and difference of the numbers indicated.Numbers Sum Difference

1) 984 207 542263 481 563

2) 725 983 654336 343 459

3) 5 963 425 3212 876 976 781

B. Read and Solve.1. A bookstore clearance sale showed that there were 40 000 books sold during the first week

and 31 968 books sold during the second week. How many more books were sold during thefirst week than the second week?

2. A certain clothes company sold the following RTW:childrens wear 165 836; ladies wear 285 360; mens wear 214 187; and unisexwear 293 579. How much did the company earn from the ready to wear (RTW) clothes?


34/371

16

Multiplying Whole Numbers


Cognitive: Review the process of multiplying whole numbersPsychomotor: Write the correct solution in multiplying whole numbers

Affective: Persevere in ones work


Skill: Review the process of multiplying whole numbersReference: BEC-PELC I.A.4.bMaterials: flash cardsValue: Patience



1. Drill

Basic facts in multiplication through flash cardsContest by pair

2. Mental Computation

Perform mentally the following:12 20 10 14 12 16

12 10 13 x 10 x 11 x 11


1. Presentation

a. Present the lesson through the use of word problem.

Each of the 45 sewers of Excellent Garments can make 1 325 pairs of socks in aweek. How many pairs can they make in all?

b. Analysis or Discussion

Ask the following:1) What is asked in the problem?2) What are given?3) What operation will be used?4) What is the mathematical sentence for the problem?

1325 x 45 = n5) Let the pupils solve the equation. Let them explain their solution on the board and

tell the complete answer.

1325x 45

66255300 .59625 pairs of socks the sewers can make in a week


35/371

17

6) Look carefully at the process:How did we get 6 625? What is the next multiplier? Why is zero (0) placed below thedigit 2 which is in the tens place? How did we get59 625? Which are the partial products? Which is the final product?

c. Provide additional examples and explain the process.d. Infusion of value (Give 1 or 2 questions.)e. Give more exercises and let pupils solve and explain the solution.

2. Generalization

To multiply whole numbers, multiply each digit of the multiplicand by each digit of themultiplier. Start with the ones digit of the multiplier. Add the partial products to get the finalproduct.

C. Application

Multiply.

IV. Evaluation

Find the product of the following. Be sure to solve accurately.

1) 40 306 2) 37 715 3) 45 681

27 53 13

Give the complete solution for each problem. Be sure to give the complete answer.

4) Mother sold 321 dozens of quail eggs. How many quail eggs did mother sell?

5) There are 25 big baskets of mango for export. If each basket contains 1124 mangoes, how manymangoes will there be for export?

V. Assignment

Read each problem. Write the mathematical sentence then solve. Be sure to give the completeanswer.

1. Mr. Rico sold 2 321 copies of mathematics books.Mr. Paz sold 12 times as many. How many mathematics books did Mr. Paz sell?

2. How much will 2 575 chairs cost at 98.00 each?3. A taxi consumes up 1 200 litres of gasoline in a month. How many litres were consumed in

one year?

Dividing of Whole Numbers


Cognitive: Review the division of whole numbersPsychomotor: Find the quotient of given numbersAffective: Perform the operation with speed and accuracy

8 364 5 022 62 008 14 342

53 14 53 34

5 629 31 695 9 009 10 312 47 43 24 35


36/371

18


Skill: Dividing whole numbersReference: BEC-PELC I.A.4.4Materials: spinner, blocks, stairs with numbersValue: Speed and accuracy



1. Mental Problem

a) We are five digit numbers and exactly divisible by 5. Who are we?b) Guess who am I? Multiply me by myself. Im almost up to fifty; though Im a little odd, Im

a bit pretty nifty. (7)c) Elmer saw 9 pigs and cows. He counted that there were 10 cows and horses. There

were 16 animals in all. How many cows were there? (3)(Pigs = 6 Cows = 3 Horses = 7)

2. Drill

Strategy: Reach the Star

Note: Give more exercises.

a) Group the pupils.b) One pupil in each group will answer one division equation. If the answer is correct, the

next pupil in the group will answer the next step. If incorrect, the next pupil will answerthe same equation until the equation becomes correct.

c) The first group to finish gets the star.


1. Presentation

Strategy 1: Problem Opener

Three boys gathered chicos from an orchard. If there were 348 chicos in the basket,how many chicos did each boy get as his equal share?

1) Ask the following:

a. What are given?b. What is being asked?c. How will you solve the problem?

1696 8896 8

96 872 8

24 8


37/371

19

2) Show by illustration how to divide 348 by 3.3) Define and identify dividend, divisor and quotient.4) Emphasize that speed and accuracy are necessary in dividing numbers.

Strategy 2: Investigatory

1. Use spinner, base ten blocks, chart, work mat

a) Spin the spinner two times and use the numbers to form a two-digit number. 26 forexample.

b) Model the number using the fewest possible base ten blocks for example.

c) Spin again to find the number of groups. Share the blocks equally using the numbershown by the spin, for example, 4. When necessary exchange ten blocks for oneblock.

d) Record your result on the work mat or in a chart as shown below. Repeat theactivity.

StartingNumber

Number ofGroups

Drawing to ShowEqual Groups

Number inEach Group

NumberLeft Over

Tens Ones Tens Ones

2 6 4

e) Describe the steps you followed to share the blocks. When did you have toexchange blocks?

f) Compare the number of blocks left over each time with the number of groups. Arethere more groups or more blocks? Explain.

Give more exercises.

2. Generalization

How will you divide whole numbers?

IV. Evaluation

A. Find the quotient.

1) 1324824 2) 1518424 3) 70823948

4) 0051023 5) 4884431


38/371

20

B. Divide then check. Do not forget to add the remainder if there is any.

1) 135923 2) 52 7332 3) 64 7872

4) 23 25576 5) 47 397532

C. Read each problem and solve:

1. Mang Berto gathered 1 350 mangoes from his orchard. Before selling the mangoes, heplaced them equally in 6 kaings. How many mangoes were placed in each kaing?

2. A rice dealer bought 1 224 sacks of rice. He hired 8 trucks to carry the rice from the provinceto Manila. How many sacks of rice were in each truck?

3. A team with 4 contestants received a cash prize of 2,448 from the Kuarta-O-Kahonnoontime show. How much did each contestant receive?

4. Last December, Lolo Carlos set aside 1,015 which he distributed equally among his 7grandchildren. How much did each child receive?

5. The cost of 24 blouses is 4,296. How much is the cost of each blouse?

One-Step Word Problems


Cognitive: Solve 1-step word problem using any of the four fundamental operationsPsychomotor: Solve accurately and correctly 1-step word problemsAffective: Develop critical thinking in analyzing and solving word problems


Skill: Solving 1-step word problems using any of the four fundamental operationsReference: BEC-PELC I.A.5.aMaterials: Charts, flash cardsValue: Thoughtfulness, critical thinking



1. Mental Computation

Drill on the basic addition, subtraction, multiplication and division facts.

Strategy 1: Relay Game Advancing Forward

Materials: flash cardsMechanics:a. Divide the class into 2 groups.

b. One member from each group will stand at the back of the room.c. As the teacher flashes a card, they answer and the one who gives the correct answer firstadvances forward.

d. The group that reaches the finish line first wins.

Strategy 2: Critical Thinking

The half of 8 is multiplied by 3 added to a number is 16. What is the number?


39/371

21

2. Review

Review the steps in problem solving.

3. Motivation

When you visit a place for the first time, what do you do before you go back home? (Buy

souvenirs for loved ones) Why do you do such a thing? Are you happy doing it?


1. Presentation

Strategy 1: Making an Organized List (Making Patterns)

Problem opener:

Nena wants to buy 3 different souvenirs. She has 100 to spend. How manydifferent combinations can she choose from?

Boardwalk Souvenirs

Mug 25.00Poster 50.00cap 50.00Key chain 25.00Handkerchief 25.00Prices include tax

a. What are the given data?b. What is asked in the problem?c. What operation are you going to use?d. What are all the possible mathematical sentences? Which 3 items cost exactly

100.00?f. If Nena wants to have a 25.00 change, which items should she buy? If she wants a

change of 50.00, which should she buy?g. Make a pattern for the possible 3 choices.

1) mug, poster, key chain2) poster, handkerchief, key chain3) cap, key chain, handkerchief4) Mug, key chain, cap5) Mug, poster, handkerchief

Valuing:If you were Nena, which would you give to your best friend? Why?

Strategy 2: Logical Reasoning (drawing patterns)

Problem Opener:

If four people eat 4 loaves of bread in 4 days, how many loaves of bread will 20 peopleeat in 20 days?a. What are the given facts?b. What is asked in the problem?c. What operation are you going to use?d. What is the correct answer?e. (Teacher should make a pattern on how to arrive at the correct answer.)


40/371

22

Strategy 3: Using a Problem Opener Preparing Tables

Study the table below then answer each question that follows.

Capiz Fun Run

DistrictGrade

Levels

Number ofParticipants in each

Grade Level

Total Number of

ParticipantsPilar 2 135 ?

Pres. Roxas 3 128 ?Panitan 4 154 ?Maayon 5 148 ?

a. How many participants came from Pilar District?b. How many participants came from Pres. Roxas District?c. Complete the table.d. What process did you use to get the total number of participants from each district?e. What steps did you follow to solve the problem?

2. Generalization

What are the steps in solving word problems?

C. Application

Solve the following problems.

1. In 1997, Mr. Martinez sold 12 496 chicken during the first quarter; 10 724 during the secondquarter, and 23 318 chickens during the third quarter. How many chickens were sold in 3quarters.

2. Mr. Sison sold 41 000 kilograms of copra in January and another 29 368 kilograms in June.How many more kilograms of copra did he sell in January than in June?

3. Each of the 4 officials of the Sports Club contributed 1,032.00 for the basketball uniforms.How much was raised for the basketball uniforms?

IV. Evaluation

Solve the following problems.1. Omar harvested 31 242 eggs. He sold 19 568 eggs to store owners. How many eggs were left

unsold?2. There were 4 grade levels which joined the parade at Luneta. Each grade level had 42 pupils.

How many pupils in all joined the parade?3. In a singing contest, the Grade V Choir won a cash prize of 4,290.00. How much was the share

of each choir member if there were 26 members?

V. Assignment

Solve the following problems.1. During the Clean and Green Week celebration, 1 246 boy scouts and 1 038 girl scouts joined in

planting tree seedlings in Antipolo Hills. How many scouters in all joined the tree planting?2. The Boracay Beach in Aklan had 45 362 Filipino local and foreign national guests last year.

If 31 625 were Filipinos, how many foreigners were there?3. Miss Lorenzo distributed 3 264 squares of cloth equally among her 16 sewers to make a table

cover. How many squares of cloth did each sewer receive?


41/371

23

Two to Three-Step Word Problems


Cognitive: Solve 2- to 3-step word problems involving any of the four fundamentaloperations

Psychomotor: Solve 2- to 3-step word problems correctlyAffective: Solve 2- to 3-step word problems involving any of the four fundamental

operations with accuracy


Skill: Solving 2- to 3-step word problem involving any of the four fundamentaloperations

Reference: BEC-PELC I.A.5.bMaterials: flash cardsValue: Accuracy, Alertness, and Cooperation



1. Drill

Drill on basic addition facts, subtraction facts, division facts and multiplication facts throughthe use of flash cards

Strategy 1: Relay Game

Mechanics:a. As the arbiter (the teacher or a bright pupil) flashes a card, the two contestants answer as

fast as they could.b. The pupil who gives the correct answer first, gets the point for his group.

c. The relay continues till at least 10 of the exercises on four fundamental operations aredone.


1. Presentation

Strategy: Problem Opener (Simplifying the Problem)

Problem # 1

Mang Ruben harvested a total of 11 380 kilograms of palay. He sold it to five differentrice dealers. If each dealer received equal amounts, how many kilograms did each one get?

If one kilogram costs 25, how much did he receive from each dealer?a. What is asked in the problem?b. What are the given facts?c. What processes are involved?d. What is the mathematical sentence?

(11 380 5) x 25 = Ne. Solve the problem.f. What is the answer?


42/371

24

Problem # 2

Last year, these were the recorded earnings of the following laborers: Mang Ignacio 22,553; Mang Cosme 19,985; Mang Rolando 29,303; Mang Baldomero 31,058; and Mang Rosauro, 21,981. What was their average earnings?

a. What is asked in the problem?b. What is the hidden problem?c. What processes are involved?d. What are the given facts?e. What is the mathematical sentence?

[( 22,553 + 19,985 + 29,303 + 31,058 + 21,981) 5] = Nf. Solve the problem.g. What is the answer?

2. Generalization

What steps should you follow when solving problems?What is the most important thing to consider in problem solving?

C. Application

Read and solve.

1. There were 407 boys and 438 girls of Rafael Palma Elementary School who joined the AlayLakad. How many buses did they hire if 65 pupils can be accommodated in a bus?

2. An egg vendor bought 600 eggs from the Soler Farm. She paid 28 per dozen. How muchdid she pay in all?

IV. Evaluation

Read and solve.

1. An airplane covered the following distances in 3 trips: 1 300 miles, 972 miles and 1 580 miles.

The average speed of the plane was 550 miles per hour. What was the average distancecovered in the 3 trips?

2. Mr. and Mrs. Lagman bought a house and lot worth 300,000 at Villa Calamba. They made aninitial payment of 60,000.00. How much was the yearly amortization if they agreed to pay for15 years.

V. Assignment

Read and solve.

1. The PTA donated 39,510 to the school to buy 15 typewriters. If each typewriter costs3,000.00, how much will the school share the total cost?

2. In the childrens store, 285 thin notebooks and 325 thick notebooks were delivered. Out of these,

190 notebooks were sold and the rest were arranged in 15 shelves. How many notebooks werein each shelf?3. The Grade V pupils went on a field trip to Tagaytay. They hired a bus for 2,445 and a minibus

for 1,235. The school gave 1,120 and the rest was shared equally by the 32 pupils. Howmuch did each pupil pay?


43/371

25

Odd and Even Numbers


Cognitive: 1. Differentiate odd from even numbers2. Identify odd and even numbers

Psychomotor: Play actively in group gamesAffective: Show alertness in playing group games


Skill: Differentiate odd from even numbersReference: BEC-PELC I.A.5.1.1Materials: concrete objects, number cardsValue: Alertness



1. Drill on discussing patterns

Write the missing numbers.a) 20, 22, 26, 32, ___, ___, ___, 76b) 4321, 4311, 4301, ___c) 68, 67, 64, 59, ___, ___, 32d) 8, 16, ___, ___, ___, 48e) 4, 9, 19, ___, ___, 159

2. Review: Skip counting

Read then do what is told.a. Skip counting by 3 from 6 to 30

b. Skip counting by 5 between 10 to 40c. Skip counting by 4


1. Presentation

Strategy 1: Use a Game The Boat is Sinking

Mechanics:a. The teacher asks the pupils to stand occupying the wide space of the room. (Number of

pupils 36)b. If the teacher gives the signal Group yourselves into 2, the pupils will group themselves

into 2.c. Teacher asks if everybody has a partner. The answer will be recorded on the board.d. The teacher repeats the signal giving another number, example into 3 and so on.e. The results will be recorded on the board.f. After giving several groupings (from 2-10), the teacher let the pupils sit on their seats.g. Analysis and discussion will be done based on the results written on the board. The

teacher must emphasize that even numbers are divisible by 2 while odd number is anumber with remainder 1 when divided by 2.


44/371

26

Strategy 2: Use of Concrete Objects

a. Show 2 objects and ask, How many groups of twos are there?b. Show 4 objects and let pupils divide them into groups of 2. Teacher asks, How many

groups of 2 are there?c. Let the pupils do the same with 6, 8 and 10 objects and teacher asks if how many groups

of twos are there.d. What have you noticed to 2, 4, 6, 8 and 10 when you group them by 2s? Is there a

remainder? Why? These are called even numbers.e. Are 12, 14, 16, 18 and 20 even numbers? Why? What are the digits in the ones place?

What are even numbers?f. Show 3 objects. Ask, How many groups of 2 are there? (groups of 2 with 1 remainder)

Do the same with 5, 7 and 9.

g. What have you noticed when you divide these numbers by 2?These are called odd numbers.

h. Are 11, 13, 15, 17 and 19 odd numbers? Why? What are the digits in the ones place?i. What are odd numbers? Differentiate even numbers from odd numbers.

Strategy 3: Charting

a. Teacher posts number cards on the chart.Ask which numbers are exactly divisible by 2.

b. Let pupils get the numbers divisible by 2.c. Teacher places these numbers in one column.d. Do the same process for pupils to identify the odd numbers.e. Teacher places these numbers in another column.f. Let pupils discover the differences between the numbers in the two columns.

Infusion of value:Do you play group games? What group games do you play? How should you play in order towin?Provide more exercises in differentiating even numbers from odd numbers.

2. Generalization

How do you differentiate odd numbers from even numbers?

Numbers divisible by 2 are even numbers. Even numbers end in 0, 2, 4, 6 and 8. Numbers when divided by 2 and have a remainder of 1 are odd numbers. Odd numbers

end in 1, 3, 5, 7 and 9.

C. Application

Write odd or even in the blank before each number._____ 1) 3104_____ 2) 263

_____ 3) 5778_____ 4) 4100_____ 5) 377

IV. Evaluation

A. Ring all even numbers and box all odd numbers.

1) 476 2) 1263 3) 70004) 1345 5) 8761


45/371

27

B. What kind of number will you get as an answer to each of the following. Write odd or even in theblank.

1) 76 + 81 = _____2) 844 + 726 = _____

3) 855 5 = _____

4) 985 x 63 = _____5) 599 - 83 = _____

C. Encircle the correct answer:If y is an odd number and x is an even number then

1) y + y = (odd, even)2) x x = (odd, even)3) y + x = (odd, even)

4) y x = (odd, even)5) x y = (odd, even)

V. Assignment

Answer each question:1. If n is an odd number and p is an even number, then p + p + n = ___.2. What will you get if you add three odd numbers and an even number?3. Give the difference between the two odd numbers right after 20. Is the difference odd or even?4. Add the consecutive even and odd numbers between 5 and 10. Is the total odd or even?

Greatest Common Factors (GCF) of Given Numbers


Cognitive: 1. Give the common factor of a given number2. Find the greatest common factors of given numbers

Psychomotor: Compute the GCF of given numbers using any methodAffective: Show cooperation with the group in finding factors


Skill: Finding the greatest common factors of given numbersReference: BEC-PELC I.A.5.1.2Materials: cards, strips of cartolina, coins, darts, boxesValue: Cooperation



1. Drill (Mental drill on Odd and Even Numbers)

Strategy: Game Flaglets Race

Mechanics:a. Divide the class into four groups. The leader gets the flags containing the words:

composite and prime number.b. Ask the first member of each group to identify the number in the cartolina strips as prime

or composite.


46/371

28

c. The teacher flashes other numbers.d. The pupil who raises the flag first gives the answer. The team gets the point if the

answer is correct. For every correct answer the flag is attached to a maze until theyreach the word finish line. If the answer is not correct, the pupil from the other team willgive his answer and get the point if his response is right.

e. Continue the game until most of the pupils have participated.f. The team who reaches first the finish line using the flaglets wins the contest.

2. Review: Factorization (Darts)

Strategy: Darts Game

Divide the class into 3 groups. Ask the first 2 memb

math five lp - pdf

Documents